## Lucas Duda’s .422 OBP and Anthony Recker’s Weird Slash Line April 28, 2015

Posted by tomflesher in Baseball.
Tags: ,
The standard error for an n-trial sample of a binary variable with probability p is $\sqrt{\frac{p(1-p)}{n}}$. If we assume Lucas’ ‘true’ OBP is .350, then the standard error of this 83-trial sample would be $\sqrt{\frac{.35(.65)}{83}} = \sqrt{\frac{.2275}{83}} = \sqrt{.00274} = .052$. That means about 66% of Lucas’s 83-plate-appearance streaks should be within one standard error, and about 95% should be within two. Due to the small sample size, it’s hard to be 95% sure that Lucas’ performance is due to actual improvement, but the upper bound of the 66% confidence window would be about .402. Lucas is outperforming that by about 20 basis points.